Justifying tense and mood morphology in counterfactuals

1.1 The role of if

Klein stresses the fact that his topic situation is not necessarily provided by an if-clause, and an if-clause needs not be topical. As we will see in a moment, the Lewis-Kratzer claim is that if doesn’t mean anything, but if-clauses simply restrict quantifiers or modals.

Additional arguments in favour of this view of if – and in favour of Klein’s approach as well – come from the observations that (a) a single if-clause (Klein’s topic situation) can modify more than one modal and (b) that if-clauses can be stacked like relative clauses. If if-then were a two-place operator, this could not be explained.

Here is an example of the first case.^[2]

The role of if might then be of carrying an anaphoric index for the then at the modal. We need an extra store for the if-clauses from which they can be taken if needed for a modal they can restrict. We cannot interpret if-clauses in situ, but for our purposes, a tensed version of Kratzer’s rule for modal restriction will do (see Section 1.3).

1.2 The main modal: would or could

The if-clause restricts some quantificational element, and the architecture of the construction depends on this operator. Here we consider the standard counterfactual modals would and could.

Importantly, despite the prevailing view in the linguistic literature from Iatridou (2000) to Klein, I will argue that it is not the past tense morphology that takes us to the remote worlds in counterfactuals, but the modal. In this respect, I will follow Lewis (1973), for whom a would-conditional amounts to the subset relation between propositions: the set of protasis-worlds which are maximally similar to the world of evaluation, is a subset of the apodosis-worlds (the relation of conditional necessity), while a could-conditional amounts to a non-empty intersection between protasis-worlds and apodosis-worlds (among the nearest protasis-worlds, there is at least one apodosis-world – the relation of conditional possibility).

There is, however, no consensus in the literature as to where and how semantic tenses fit into this picture.

Arguably, a tensed version of Lewis’ analysis will have the following truth-conditions:

Modals embed a non-finite clause (“the prejacent”). Like all other verbs, modals have a time argument. The semantics of modals contains the information that the prejacent is to be evaluated in the accessible worlds at the local evaluation time of the modal. Thus, modals are verbs of temporal control.

1.3 Temporal control

Counterfactual conditionals give rise to a structure at logical form (LF) in which the temporal proposition expressed in the protasis restricts the domain of quantification of the modal operator would/could, which takes the temporal proposition (the prejacent) in the apodosis as its argument.

Lewis’ two separate modals are interpreted with respect to a similarity relation ≤ that orders the accessible worlds with respect to the local evaluation world w: w₁ ≤_w w₂ means that w₁ is at least as similar to w as w₂. Our innovation is the temporal control: the variable t has three bound occurrences in the meaning representation:

Would and could are one-place operators. Like any other verb they have a temporal variable. For the (metaphysical) accessibility relation R, see Lewis (1979). We have to relativize R to time, a point also made by Ippolito (2003) and others. Which worlds are accessible depends on the local evaluation time. In other words, the accessibility relation R gives us different facts at different times because we know different facts at different times.

Klein makes an important point that the “counterfactuality” expressed by would does not mean “false in the actual world”. In fact, without further restriction, the Lewisian one-place modals don’t add anything to the content. This is so because at each time t every world that is maximally similar to the local evaluation world while having the same past is the local evaluation world itself. This trivialization of the modals might be the reason for why we virtually never use them without a restriction (an if-clause).

I would think this is the key to an explanation for what Klein calls “the missing modus ponens” (see also Bennett 2003). According to Klein, from a counterfactual conditional If the light were red, it would be too late, we cannot add (Now,) the light would be red, and then proceed to (Hence), it would be too late.

Indeed, it is hard to have intuitions about unrestricted counterfactual modals without Klein’s contextually provided topic situation. What does the isolated sentence Now, the light would be red actually mean? Klein – following Kratzer – still has a good point that the if-clause is not necessary for a counterfactual statement. It is an optional addition.

What is important for the tense-mood-system is that whenever we have an if-clause (or something similar) as a restrictor to the modal, we get temporal control in the sense that the subordinate time variable is bound from the matrix.

Semantic control is built into the meaning of the modals in (11) above. The semantic type of the prejacent must be a temporal property, and this must also be the type of the protasis. From the paraphrase in (13), we see that the if-clause is evaluated at the local evaluation time of the modal (“now”):

This is not an independent, deictic ‘now’, but a bound time variable. The protasis and prejacent of the modal are tenseless propositions interpreted via λ-conversion as if they contained a deictic present.

The highest semantic tense in the protasis will always be semantically empty, called TPRO (a covert temporal pronoun) in Grønn and von Stechow (2010). TPRO is also the highest embedded tense under attitudes in this theory. In both cases, we can apply S(equence)O(f)T(ense)-rules.

In order to get this machinery working, the if-clause is combined with the modal via a special rule, which is similar to the rule that combines a relative clause with its head noun, i.e. Predicate Modification. We call this rule Modal Modification:

This is a tensed version of Modal Restriction given in Kratzer (1981, 2012. The rule has an inbuilt temporal control device. The semantics of the modal and the rule MM force us to have bound tense in the if-clause. Otherwise, we would have a type mismatch.

We can reconstruct one or several if-clauses to a position adjacent to and c-commanded by the modal. If one if-clause modifies several modals, we simply copy it to the adjunct positions of the modals that are to be modified. Thus, the if-clause is subordinated to the modal at LF, and we have in fact regained the structural configuration from which we started in (5) and (6) above.

2.1 Fake past

The most controversial issue in tense semantics for conditionals is the interpretation and analysis of the past tense morphology in would and would have-conditionals.

Klein adheres to a view popularised in Iatridou (2000): past tense morphology has an exclusion feature (ExclF) and points to a remoteness operator (<) in the temporal or modal domain.

The idea underlying these approaches is that the semantic Past brings us either to a remote (past) time or to a remote world. It is not obvious how the modal version should be spelled out. A merit of Schulz (2014) is that she makes the idea precise: In her technical implementation, the would-conditional brings us a little bit away from our world w0; the would have-conditional brings us even farther. Temporally, both conditionals are semantically present since the modal past and real past are in complementary distribution. See also Schlenker (2004) for an explicit analysis along these lines.

The idea is nice, but if the past and perfect can be world shifters, then this raises the question where the quantification over worlds comes from. What would be the role of the necessity modal would versus the possibility modal could in such a system?

The modal approach also faces the problem that would-have-conditionals end up being semantically present. Empirical evidence from temporal adverbials shows that unlike ordinary would-conditionals, they are semantically past statements in most cases:

Finally, as pointed out also by Klein, a theory – like the past-as-modal approach – which asserts or presupposes that the protasis in would-have-conditionals is untrue in the actual world, will, obviously, have a problem with so-called Anderson-conditionals.

Thus, the approach that I will defend here rejects the idea that the semantic past brings us to a remote world. For an adequate analysis, one arguably has to separate quantification over worlds from quantification over times. The first is done by verbal quantifiers (modals), the second is done by semantic tense operators.

In our approach, counterfactual would quantifies over worlds, but there is more to it: would is a universal quantifier, we have a special accessibility relation and we have to distinguish this modal from the counterfactual possibility modal could. The past-operator cannot do all these things alone. Furthermore, the evaluation of would can be shifted to a past time in would-have-conditionals. This would not be possible if the local past shifted the evaluation simply into remote worlds.

2.2 Real and fake perfect

The temporal structure of most English modals is obscured by the fact that they only have finite forms and have lost their non-finite counterparts. Accordingly, there is no transparent way to express a past tense modal (“#must-ed”). Most modals, including the subjunctive modals could, should, ought and would, must be shifted to a past time through the presence of an embedded infinitive perfect. At LF, we have the semantic perfect have above the finite modal. In a truly past counterfactual conditional, the perfect is therefore like a past:

The main function of this perfect is to locate the necessity or possibility modal in the past by restricting the time variable of the accessibility relation of R.

A transparent semantics wants to have the perfect auxiliary above the modal. German or French surface syntax is parallel to a transparent logical form, while English is misleading: The surface syntax reverses the expected hierarchical order with the modal above the perfect auxiliary. At LF, we have to switch the relative hierarchy:

In Arregui (2009) would-have-conditionals are analyzed in situation semantics. In that theory, would-have-conditionals are out-scoped by a semantic past (denoting a particular situation).

Semantically, the two approaches come to the same, but the compositional contribution of have is obscure in Arregui’s approach.

In the theory sketched here, we allow for the perfect also to have local scope inside the apodosis (20) or protasis (21):

The main semantic tense in both cases is the present. The local perfect in counterfactual conditionals can have different flavours (relative past, resultative perfect or extended now) depending on your favourite theory for the perfect (Grønn and von Stechow 2020).

Arregui (2007) provides some counterexamples to a treatment of would have-conditionals as having a perfect (relative past) out-scoping the bare conditional. Her examples involve real perfects which seem to occur locally in the conditional. This is precisely the kind of examples we have in mind when we acknowledge the presence of local perfects in the protasis and apodosis.

Arregui analyzes have as a stativizer. In Grønn and von Stechow (2020), we argue that the perfect can also be a relative past (anteriority reading) or extended now (true perfect). In this respect, our account is different from the one in Arregui (2007).

But there is yet another reading of the perfect: the identity reading, or the fake/empty auxiliary.

Note that had in the protasis does not contribute to the meaning. This is one of the mysteries of the protasis in ordinary would have-conditionals: Both layers of past in the protasis in (22) are in a sense tenseless.

We thus have three structures where the perfect is involved:

1. A relative past have in the apodosis out-scopes would at LF, and had in the protasis is semantically fake.

2. A real perfect have remains in the scope of would, i.e. the entire conditional is out-scoped only by NOW, cf. ex. (20).

3. A real perfect had is interpreted locally inside the protasis, i.e. the entire conditional is out-scoped only by NOW, cf. ex. (21).

3.1 Present counterfactuals

Here is an LF and feature analysis of a concrete example:

Counterfactual modals like would are treated as overt, semantic operators which carry the interpretable feature combination i-past, i-subjunctive. The modal does not have an inherent morphological uF. In the example above, the temporal variable of the modal, the time of the accessibility relation R, receives a present tense feature (u-n) from the deictic NOW. Semantically, the construction is therefore present. The u-now feature on the operator is blocked there and not transmitted any further because it is in conflict with i-past of the same operator. Due to temporal control, the present interpretation still gets into the if-clause and the prejacent.

In the semantic binding domain of would, we encounter the form were in the if-adjunct. Recall from Section 1.3 that temporal control is inherited by the adjunct clause through modal modification. The verb form were has two inherent morphological features, past and subjunctive, which appear as u-features on the temporal variable t₂ where they can be checked against the i-features of would. Hence, the past subjunctive of were is licensed and semantically empty. We have basically applied the SOT-rules from Grønn and von Stechow (2010).^[4]

Let me enumerate five relevant principles behind the feature system in view of what we have just seen:

1. An iF of a semantic operator (e.g. i-past, i-sub of would) is transmitted under binding as an uF to a variable bound by the operator.

2. For each lexical entry with an inherent uF (e.g. u-past, u-sub of were), there must be an overt or covert semantic operator with a corresponding iF (e.g. i-past, i-sub of the overt would).

3. An iF of an overt operator does not require the presence of an inherent uF in its semantic domain. A clear case is i-sub of would, which only has a function in the system when the form were with the inherent feature u-sub surfaces in the if-clause. Typically, we find indicative past forms in the protasis, and [sub] is then neutralised.

4. Verbs, adjectives and operators in general transmit features to the variables they bind provided there is no competition with an inherent i-feature of the operator. Thus, if an operator has a feature iF and it inherits uF′ via binding, it does not transmit uF′ into its semantic domain. For example in (23), would inherits the feature (u-n) which is in conflict with its own semantic tense feature i-past. The feature (u-n) is therefore not transmitted further.

5. Lexical entries can be unmarked with respect to F. The counterfactual modals would, could, non-finite verbs etc. don’t have inherent, morphological u-features.

3.2 Past counterfactuals

If-adjuncts under verbal quantifiers like would are subject to the SOT-parameter, but that is not enough to explain away the second layer of past tense in the protasis of Germanic and Romance languages.

How is the perfect auxiliary justified? The problem with this construction is that had in the if-clause must be semantically void, because the matrix have shifts the entire construction into the past and the if-clause is not temporally back-shifted with respect to the main clause. In some sense had is an agreement phenomenon with the shifting of would toward the past.

The special status of these constructions is evident from the existence of a separate paradigm in Romance – the conditional has its own grammar. Hence, we should not be too surprised to find construction specific rules. The stipulation in the LF for (24) is simply that had in this construction comes with a u-perf feature^[5] and is licensed and deleted by i-perf under binding. This is how we express the idea that had is in a pure agreement with the matrix have.

In other words, when we do the standard decomposition of had as Past + have, our account says that the first layer is deleted as a fake past, and the other layer is uninterpreted as well.^[6]

The assumptions made so far are not sufficient to rule out sentences with a simple past in the protasis as a would-have-conditional:

The feature checking is OK in accordance with the predictions of our system. The sentence has precisely the meaning one wants for a would-have-conditional, and it doesn’t contain the semantically inert had, which we find in Klein’s original example (22). Still, (22) is clearly preferred over (25). The construction without had is not accepted by school grammars.

The construction with an empty/fake if…had is found in most Germanic and Romance languages, and is presumably a pragmatic/stylistic phenomenon: a device to signal that have in the apodosis must have scope over the main modal. If a deeper motivation for the presence of the auxiliary in the protasis could be given, that would point to a weakness of our account.

3.3 Some interesting properties of would under attitudes

The feature i-past originating with an operator would that is not a semantic past, encodes the fact that we observe tense transposition in counterfactual conditionals, i.e. statements that look like past statements are semantically present. Similarly, we expect that counterfactual conditionals that look as if they were pluperfect statements are past statements. This is what we find in ordinary would-have-conditionals.

From the point of view of feature assignment, could is analysed exactly as counterfactual would. However, as Klein points out, there are other versions of would, e.g. the temporal would, known from school grammar as the future in the past. Let’s call the latter would2 and distinguish it from the counterfactual would1. Semantically, the forward shifter would2 is the mirror operator of the relative past, the backwards shifting perfect we encountered in (17) above.

However, there is an interesting difference in the u-features between the lexical entry in (26) and the matrix use of had. Therefore, I cannot fully agree with Klein when he writes about the temporal would2 that “it can designate a time after a past time, just as the pluperfect designates a time before a past time”.

Unlike the pluperfect, would2 is typically blocked in main clauses:

In our system, the difference between would2 and had is explained by the features. The temporal auxiliary had carries a feature u-past which is checked by a covert operator PAST with the feature i-past. On the other hand, would2 has the inherent feature combination u-past, u-sub, but there is no subjunctive operator in (28) that could license u-sub.

So when do we use would2? Under past attitude verbs (Abusch 1997)!

Attitude verbs are known to be intensional and embed temporal properties; hence we get the following feature distribution in a standard SOT configuration:

The feature i-sub on the attitude verb, an overt operator, is normally not articulated by morphology in the complement clause in English and can be ignored (cf. principle P3 in Section 3.1), but in (29/30) we clearly need it to license would2 in the complement.

Attitude verbs and their complements can also inform us in non-trivial ways about the temporal properties of the counterfactual would1.

Recall that the counterfactual operators would1/could have the feature combination i-past, i-sub. We know (also from the discussion in previous sections) that counterfactual would1/could cannot have an inherent/morphological u-past feature since the construction cannot be modified by a past time adverbial:

Works in tense semantics within this framework, e.g. von Stechow (2009) and Grønn and von Stechow (2016), have established that the covert semantic operator PAST must be made visible through a corresponding inherent morphological u-past.^[7] The features would be OK in (31), but it is an empirical fact that the configuration does not exist in English. Hence, would1 cannot have an inherent u-past feature.

Now comes the interesting point. We have seen that would1 is semantically present in Klein’s examples, but could would have an inherent present feature u-now? The answer is no, as we see from counterfactual conditionals embedded under past attitudes:^[8]

In (32), the temporal variable of would1 must receive the feature u-p from the matrix PAST, the closest temporal operator. There is no other option. This shows that would1 cannot be an inherent present despite our informal talk of would-conditionals as being semantically present. Furthermore, if would1 were inherently present, we would expect to encounter the special double access reading since this is what is observed for present tense complements under past attitudes in English (Abusch 1997). But this is not what we find in (32). The conditional only has a simultaneous reading with the attitude verb.

Note also that the embedded would1-conditional in (32) cannot be backwards shifted under the past attitude, which would be expected as a possible reading if would1 had an inherent u-past feature. So in some sense, counterfactual would (could) must be semantically tenseless, i.e., it cannot be classified as a plain present or as a plain past. It follows from this that we can insert the same counterfactual also under the present form believes in (33). The feature distribution is different, but we obtain the same simultaneous reading as in (32):

The system presented here can account for the empirical fact that neither the modal nor temporal would can be immediately bound by a semantic PAST, but both are perfectly fine under past attitudes. The modal would1 is tenseless and cannot make i-past visible on past; the temporal would2 has a u-sub feature that must be licensed in addition to u-past.

To sum up, we have developed a feature system using the following time and mood features, which arguably play an essential role in counterfactual conditionals:

1. [i-n] originates with the semantic present N.

2. [i-p] originates with the semantic past and counterfactual modals like would and could.

3. [i-sub] originates with verbs of attitude and counterfactual modals like would and could.

4. [i-perf] originates with the temporal auxiliary have.

Klein makes a point that an approach looking only at the overall meaning of the construction, say, the truth-conditions of counterfactual conditionals, could be “disastrous for the linguist who has to explain how this overall meaning results from its components”. This is why I have dragged the reader of this commentary into the tedious details of semantic and morphological features at the interfaces.